In a device disclosed in German patent document 198 26 047, each valve actuator, whose actuating piston is joined in one piece with the valve tappet of the allocated gas-exchange valve, is permanently connected with its first working chamber to a fluid-pressure source delivering fluid under high pressure, and with its second working chamber is connected, on one hand, to a first electric control valve alternately closing or releasing a supply line to the fluid-pressure source, and on the other hand, is connected to a second electric control valve alternately releasing or closing a discharge line leading to a fluid reservoir. The electric control valves are designed as 2/2-way solenoid valves having spring resetting. When the gas-exchange valve is closed, because of the first working chamber connected permanently to the fluid-pressure source, and because of the second working chamber separated from the fluid-pressure source by the first electric control valve and connected to the discharge line by the second electric control valve, the actuating piston of the valve actuator takes its normal position. Both electric control valves are switched over to open the gas-exchange valve. In this manner, on the one hand, the second working chamber of the valve actuator is blocked with respect to the discharge line by the second electric control valve, and on the other hand, is connected by the first electric control valve to the supply line to the fluid-pressure source. Since the actuating-piston surface delimiting the second working chamber in the valve actuator is larger than the actuating-piston surface delimiting the first working chamber, the actuating piston moves out of its normal position, accompanied by reduction in the volume of the first working chamber, and thereby opens the gas-exchange valve. The size of the opening lift is a function of the formation of the electric control signal applied to the first electric control valve, and the opening speed is a function of the fluid pressure applied from the fluid-pressure source. To maintain the gas-exchange valve in a specific open position, the first electric control valve is subsequently switched over, so that it blocks the supply line to the second working chamber of the valve actuator. In this way, all open positions of the gas-exchange valve may be adjusted by an electric control unit for generating control signals. The gas-exchange valve is closed by resetting the second electric control valve into its open position, so that the first working chamber of the valve actuator is again connected to the discharge line. To control a gas-exchange valve, in each case two electric control valves are necessary which act upon the second working chamber of the allocated valve actuator with fluid pressure, or relieve it of pressure, accordingly.